Exploring the BSM parameter space with Neural Network aided Simulation-Based Inference

TL;DR

This work tackles the computational bottleneck of exploring high-dimensional BSM parameter spaces under stringent experimental constraints by applying amortized neural Simulation-Based Inference (SBI) methods. It compares Neural Posterior Estimation (NPE), Neural Likelihood Estimation (NLE), and Neural Ratio Estimation (NRE) on pMSSM5 and pMSSM9 with Higgs, flavor, and dark matter observables, using the Test of Accuracy with Random Points (TARP) for validation. The results show that NPE consistently yields faithful posterior distributions with far fewer simulations and substantially less wall-clock time than MCMC, while NLE and NRE underperform in this setting. Including dark matter constraints in the 9-parameter study demonstrates strong pruning of parameter space and reveals DM-dominated regions (bino up to ~1.5 TeV, wino ~1.5–2 TeV), highlighting SBI’s practical value for rapid, reliable beyond-Standard-Model inferences.

Abstract

Some of the issues that make sampling parameter spaces of various beyond the Standard Model (BSM) scenarios computationally expensive are the high dimensionality of the input parameter space, complex likelihoods, and stringent experimental constraints. In this work, we explore likelihood-free approaches, leveraging neural network-aided Simulation-Based Inference (SBI) to alleviate this issue. We focus on three amortized SBI methods: Neural Posterior Estimation (NPE), Neural Likelihood Estimation (NLE), and Neural Ratio Estimation (NRE) and perform a comparative analysis through the validation test known as the \textit{ Test of Accuracy with Random Points} (TARP), as well as through posterior sample efficiency and computational time. As an example, we focus on the scalar sector of the phenomenological minimal supersymmetric SM (pMSSM) and observe that the NPE method outperforms the others and generates correct posterior distributions of the parameters with a minimal number of samples. The efficacy of this framework is tested on 5 parameter pMSSM with Higgs and flavor physics data and its performance is compared with the MCMC method. We further add dark matter (DM) observables to make the task more challenging and consider a 9 parameter pMSSM. We observe that even though the efficiency factor drops, the amortized SBI method still produces faithful posterior distributions. SBI predicted points satisfying DM constraints are mostly bino-dominated upto $\sim$ 1.5 TeV, and are mostly wino-dominated within the 1.5 - 2 TeV range.

Figures (13)

• Figure 1: The flowchart of all the three SBI algorithms i.e., NPE, NLE and NRE is displayed in this figure.
• Figure 2: Distributions of all the 14 observables in training sample after adding the noise are displayed. The orange-brown histograms represent the simulated training sample distribution whereas the dashed blue lines indicate the true value of each observable.
• Figure 3: TARP test plot corresponding to $1\times 10^4$, $3\times10^4$, $5\times10^4$, $1\times 10^5$, $1.5\times10^5$, $2\times10^5$ sample subsets with NPE method are displayed here.
• Figure 4: TARP test plot corresponding to $2\times 10^5$ sample subset for NLE (Left) and NRE (right) method are displayed here.
• Figure 5: The comparison of posterior sample efficiency (left) and the time taken for different sample subsets corresponding to three different algorithms is displayed here.